Informational Interpretation of Standard Algebraic Structures

Abstract

In this chapter we discuss relationships between some structures with information operators presented in Chap. 4 and various standard algebraic systems of algebraic logic. These relationships are of the two kinds. First, we show that structures with information operators can be equipped with some standard algebraic structures, thus obtaining an informational example of the underlying classes of algebras. Second, in some cases we present an informational representation theorem for a standard class of algebras, namely, a theorem of the following form: every algebra from the given class of algebras is isomorphic to a subalgebra of an algebra determined by a structure with information operators.